Geometrical control of the magnetization direction in high aspect



Geometrical control of the magnetization direction in high aspect
PHYSICAL REVIEW B 78, 012408 共2008兲
Geometrical control of the magnetization direction in high aspect-ratio PdNi ferromagnetic
J. C. Gonzalez-Pons, J. J. Henderson, and E. del Barco*
Department of Physics, University of Central Florida, 4000 Central Florida Boulevard, Orlando, Florida 32816-2385, USA
B. Ozyilmaz
Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542
共Received 10 June 2008; published 18 July 2008兲
We present a study of electron-beam evaporated Pd0.4Ni0.6 alloy thin films by means of ferromagnetic
resonance measurements on extended films of varying thickness and anisotropic magnetoresistance measurements of lithographically patterned high aspect-ratio ferromagnetic electrodes, respectively. The results reveal
that the direction of the magnetization strongly depends on the electrode lateral dimensions, transitioning from
in-plane magnetization for extended films to out-of-the-plane magnetization for electrode widths below 2–3
microns, reaching ⬃58° off plane for 100 nm-wide nanoelectrodes.
DOI: 10.1103/PhysRevB.78.012408
PACS number共s兲: 75.70.⫺i, 76.50.⫹g, 75.47.⫺m, 72.25.⫺b
Recently Pd1−xNix alloy has attracted considerable attention as ferromagnetic electrodes in carbon-based lateral spin
valves. Its excellent wetting properties on carbon nanotubes
共CNTs兲 共Refs. 1–3兲 lead to low ohmic contacts 共transparent兲,
while its room-temperature ferromagnetic behavior4 provides
a means for spin injection. Surprisingly in the case of CNTs
a tunneling barrier between the PdNi and the CNT itself
seems not to be necessary for spin injection, making PdNi
alloys the ideal material for magnetic electrodes in low dimensional carbon-based electronic devices. Key to these experiments is anisotropy, since the successful demonstration
of spin injection is based on the observation of a giant magnetoresistance 共GMR兲 effect,5 which is determined by the
relative orientation between the magnetization of the two
ferromagnetic electrodes in a spin-valve device. In particular,
it has been shown that in all-metallic spin valves in which
the magnetization vectors of both ferromagnets are not collinear 共0 ⬍ ␪ ⬍ 180兲, the current-induced switching of the
magnetization state of the device can be obtained in much
shorter times, making them highly efficient systems for information processing.6 In carbon-based spin-valve devices
the planar arrangement of the system complicates the realization of noncollinear magnetizations, and the ability to
control the magnetization direction with respect to the plane
of the electrode becomes essential. However little is known
about the magnetic properties of such ferromagnetic alloys
when lithographically patterned into narrow electrodes with
large aspect ratios. A detailed understanding of the magnetic
characteristics of this material is therefore crucial to both
understand the switching characteristics of such a device and
optimize the electrode dimension and configuration when
used as ferromagnetic spin injectors.
In this Brief Report we present a detailed study of the
effect of the geometry of electron-beam patterned Pd0.4Ni0.6
ferromagnetic thin-film structures on the equilibrium direction of the magnetization with respect to the film plane. For
extended films, room-temperature ferromagnetic resonance
共FMR兲 measurements show that the magnetization remains
in the film plane preferentially for 4–80 nm-thick films. A
substantial out-of-the-plane uniaxial anisotropy which tends
to pull the magnetization off plane competes with the demag1098-0121/2008/78共1兲/012408共4兲
netizing fields which set the magnetization in-plane. For laterally constrained large aspect-ratio Pd0.4Ni0.6 thin-film electrodes, anisotropic magnetoresistance 共AMR兲 transport
measurements show that the magnetization cants out of the
film plane for electrode widths below ⬃2 – 3 ␮m, reaching
an angle with respect to the film plane of ⬃58° for electrode
widths down to ⬃100 nm.
Pd0.4Ni0.6 alloy extended films were fabricated by
electron-beam evaporation of the bulk material on Si/ SiO2
wafer in a UHV system with a base pressure of 7
⫻ 10−7 Torr. In addition, 25 nm-thick Pd0.4Ni0.6 films were
patterned in the shape of high aspect-ratio electrodes of
length 20 ␮m and various widths 共100 nm− 10 ␮m兲. In a
second lithographic step the PdNi electrodes were contacted
with standard Ti/Au electrodes 共5/50 nm兲 necessary for
transport measurements.
FMR measurements were carried out at room temperature
with a high-frequency broadband 共1–50 GHz兲 microcoplanar-waveguide 共␮-CPW兲 共Ref. 7兲 using the flip-chip
method.8–10 A 1.5 T rotatable electromagnet was employed to
vary the applied field direction from the in-plane 共␾ = 0°兲 to
normal to the film plane 共␾ = 90°兲 directions. The change of
the resonance field value of the 15 GHz FMR absorption
peak as a function of the relative angle between the external
magnetic field and a 20 nm-thick NiPd film is shown in Fig.
1. The inset of the figure is a geometrical representation of
the applied magnetic-field vector and the angle, ␾, that was
rotated through. Also the inset of Fig. 1 shows two absorption curves corresponding to two orientations of the field,
␾ = 0 共in-plane兲 and 90° 共out-of-the-plane兲. Similar behavior
was observed for all the studied films. The data are typical of
polycrystalline ferromagnetic films with in-plane
magnetization.9,11 The resonant field value is lowest at 0 or
180°, when the applied field is in the same plane as the
magnetization vector.
The magnetic energy of a ferromagnetic film in the presence of a magnetic field, H, applied at an angle, ␾, with
respect to the plane of the film is given by9,11
E = − M sH共cos ␾ cos ␾m + sin ␾ sin ␾m兲 + 2␲ M s2 sin2 ␾m
− 共K1 + 2K2兲sin2 ␾m + K2 sin4 ␾m ,
where M s is the saturation magnetization, ␾m is the angle
©2008 The American Physical Society
PHYSICAL REVIEW B 78, 012408 共2008兲
f = 15GHz
t = 20nm
between the magnetization and the film plane, and K1 and K2
are the first- and second-order out-of-the-plane uniaxial anisotropy constants, respectively. The first term represents the
Zeeman energy associated with the coupling of the magnetization and the external field, which tries to align both along
the same direction. The second term is the magnetostatic
energy, which forces the magnetization into the plane. The
last terms represent the out-of-the-plane uniaxial anisotropy,
which minimizes the energy in a direction normal to the
plane. The final orientation of the magnetization of the ferromagnetic film results from a competition between these
three energies. The data in Fig. 1 can be fitted using the
equation of condition of resonance given by the Smit and
Beljers formula,12 ␻ = ␥冑H1H2, where ␥ = g␮B / ប is the gyromagnetic ratio, and H1 and H2 depend on H, ␾m, ␾, M s, K1
and K2 共see Refs. 9 and 11 for the exact expression兲. A good
fitting of the data in Fig. 1 共continuous line兲 is obtained for
M s = 290 emu/ cm3 共according to a 60%-Ni composition
with magnetization density M sNi = 485 emu/ cm3兲, g = 2.22,
K1 = 2.26⫻ 10−5 erg/ cm3, and K2 = 0.22⫻ 10−5 erg/ cm3.
When the field is applied at ␾ = 0 or 90°, the resonance
condition reduces to
= Hres共Hres + 关4␲ M eff兴储兲,
= Hres − 关4␲ M eff兴⬜ ,
(Meff)⊥ = 2.31kG
t (nm)
HR (kG)
FIG. 1. Behavior of the FMR peak position of a 20 nm-thick
Pd0.4Ni0.6 film as a function of the angle of application of the magnetic field from the plane of the field upon application of 15 GHz
microwave excitation. The sketch at the bottom of the figure represents the experimental configuration of the sample, which is placed
upside down on top of the ␮-CPW transmission line. The magneticfield direction is also indicated. The inset on the left shows the
corresponding FMR absorption versus field for angles ␾ = 0 and
φ (degrees)
(Meff)// = 1.85kG
H ⊥ film
H // film
t = 20nm
Ki (10 erg/cm )
9 10
s lo
γ2 2
H (kG)
f /H (GHz /G)
HR (kG)
f (GHz)
where 关4␲ M eff兴储 = 4␲ Ms − 2K1 / M s − 4K2 / M s, and 关4␲ M eff兴⬜
= 4␲ Ms − 2K1 / M s. According to this, the difference between
FIG. 2. Frequency behavior of the FMR peak of a 20 nm-thick
Pd0.4Ni0.6 film in the parallel 共left axis, solid data兲 and perpendicular 共right axis, open data兲 configurations, respectively. The inset
shows the first- 共K1兲 and second- 共K2兲 order out-of-the-plane
uniaxial anisotropies as a function of the film thickness.
the frequency dependences of the FMR peak in the parallel
and perpendicular configurations 关see Eq. 共2兲兴 enables an independent determination of the anisotropy parameters. The
longitudinal and perpendicular frequency behaviors of the
FMR peak of a 20 nm-thick film are shown in Fig. 2. The
slope of the curves allows the determination of the gyromagnetic ratio, hence the Landé g-factor,13 while the intercept
with the x axis gives the effective in-plane and out-of-plane
magnetizations, 关共4␲ M eff兴兲储 and 关共4␲ M eff兴兲⬜. The difference
observed between the two effective demagnetization fields is
indicative of the presence of a second-order anisotropy term,
which can be deduced from 共关4␲ M eff兴储 − 关4␲ M eff兴⬜
= 4K2 / M s兲. The thickness dependence of the first- and
second-order anisotropies, K1 and K2, extracted by this
method is shown in the inset of Fig. 2. The results indicate
that the out-of-plane 共K1, K2 ⬎ 0兲 easy-axis anisotropy first
decreases with increasing film thickness, for thickness values
below 10 nm, and reaches a minimum 共K1 = 1.3
⫻ 10−5 erg/ cm3兲 at t = 10 nm. K1 then increases up to 2.9
⫻ 10−5 erg/ cm3 for a film thickness of 25 nm, above which
it becomes practically thickness independent 共results obtained up to 80 nm, not shown here, support this evidence兲.
The magnetic quality factor of the thin film is defined as the
ratio between the anisotropy energy and the demagnetizing
共magnetostatic兲 energy, Q = 共K1 + K2兲 / 2␲ M s2. In the limit of
Q ⬍ 1, the demagnetization field dominates over the out-ofthe-plane anisotropy. For the thicknesses studied here we obtain Q ⬍ 0.7, in agreement with the in-plane alignment of the
magnetization extracted from the angular dependence of the
FMR field. In general, the demagnetizing field vector is determined by the shape of the sample and characterized by the
demagnetizing factors Nx, Ny and Nz, with Nx + Ny + Nz = 4␲.
In the case of an extended thin film, the only component of
the demagnetizing field is normal to the plane 共i.e., Nz = 4␲
and Nz = Ny = 0兲, and will strongly oppose to the magnetization to tilt away from the film plane.
AMR measurements were performed in laterally con-
PHYSICAL REVIEW B 78, 012408 共2008兲
AMR (%)
∆L / (∆L+∆P)
(L) longitudinal
sample 1
sample 2
(T) transverse
(P) perpendicular
Q <1(0.7)
Q >1
H (T)
∆T / ∆P
FIG. 3. 共Color online兲 Room-temperature AMR response of a 25
nm-thick, 250 nm-wide, 10 ␮m-long Ni0.6Pd0.4 electrode as a function of an external magnetic field applied in the directions indicated
in the figure. The inset on the left shows an AFM image of the
strained Pd0.4Ni0.6 large aspect-ratio electrodes 共i.e., nanowires兲 of thickness t = 25 nm, length l = 20 ␮m, and widths
varying from 100 nm to 10 ␮m. An AFM image of one of
the electrodes is shown in the inset of Fig. 3. The magnetoresistance varies as a function of the relative angle between the
applied electrical current and the magnetization vector, M
ជ and ជI are
The largest 共lowest兲 resistance is obtained when M
collinear 共perpendicular兲.14 The magnetoresistance is proportional to cos2共␪兲,15 where ␪ is the angle between the magnetization and the current, which in our case flows along the
length of the nanowire. Yet, the direction of the magnetization is determined by the direction and strength of the applied magnetic field, the intrinsic uniaxial anisotropy, and the
demagnetizing field of the film, which will in turn depend on
the geometry 共width兲 of the nanowire.
The AMR curves obtained with the external dc field applied along three different directions relative to the electrode
geometry are shown in Fig. 3 for a 25 nm-thick Pd0.4Ni0.6
electrode 250 nm wide and 20 ␮m long. The largest change
in resistance, a 0.68% increase in the AMR at saturation, is
observed when the magnetic field is aligned along the axis of
the electrode 共L兲. On the contrary, when the magnetic field is
oriented perpendicular to the film, only a 0.352% decrease in
the AMR is observed. In both cases, the saturation of the
AMR response is achieved for fields over ⬃2 kG, in agreement with the value of the effective demagnetizing fields
observed by FMR in extended films 关Figs. 2共a兲 and 2共b兲兴.
However, when the field is oriented across the wire there is
no appreciable change in AMR with field for this particular
electrode width, for field values as high as 8 T. This is indicative of a modified demagnetizing field vector imposed by
the constrained lateral dimension of the structure, which prevents the magnetization from orienting across the wire. For
widths larger than 2 – 3 ␮m, the transverse AMR saturates at
the same value as the perpendicular AMR, as will be discussed below.
One can extract information about the direction of the
magnetization by looking at the absolute change in AMR for
w (µm)
FIG. 4. 共a兲 Normalized longitudinal AMR change as a function
of the electrode width. The open circles were taken on a second
sample that was fabricated independently. 共b兲 Ratio between the
transverse and perpendicular AMR changes as a function of the
width. The sketch in the middle represents the orientation of the
magnetization with respect to the film plane for different electrode
different field orientations. In the case of the electrode shown
in Fig. 3, the fact of having the largest AMR change when
the field is applied along the nanowire axis, ⌬L = 0.68%, is
indicative of an initial magnetic configuration in which most
of the spins were aligned away from this direction, contributing to a large increase in the device resistance when aligning with the current by the action of the longitudinal field
共L兲. In addition, the smaller AMR change 共decrease兲 with the
field applied perpendicular to the film plane 共P兲 is an indication of the fact that most of the spins were already close to
this orientation before the field application. Since for this
particular nanowire there is no change in magnetoresistance,
⌬T = 0, when the field is applied transversally to the wire 共T兲,
we can assume that all the spins are located in the L-P plane.
In this situation and assuming a rigid magnetization vector,
the normalized AMR in the longitudinal direction, ⌬LN
= ⌬L / 共⌬L+⌬ P兲, can be understood as the projection of the
magnetization along the P axis. Consequently, one can estimate the angle between the magnetization and the film plane
using ␾m = sin−1共⌬LN兲, which for the 250 nm wire in Fig. 3
corresponds to ␾m = sin−1共0.787兲 ⬃ 52°.
Figure 4共a兲 shows the normalized longitudinal AMR
change as a function of the electrode width, w. It can be
observed how the longitudinal AMR change reaches its
maximum value 共⌬LN ⬃ 0.85兲 for a 100 nm nanowire. Following the previous arguments, this corresponds to an angle
of 58° between the magnetization and the film plane. ⌬LN
gradually decreases with increasing widths until it arrives at
a final value of 0.5 for widths over 2 – 3 ␮m. Before going
PHYSICAL REVIEW B 78, 012408 共2008兲
into a detailed discussion about the magnetic configuration
of the widest electrodes it is important to note that for electrode widths over ⬃1 ␮m there starts to appear a change in
the transverse AMR, ⌬T, which eventually arrives at the
same saturation value as the perpendicular AMR change, ⌬ P,
for widths over 3 ␮m. This indicates that the transverse direction 共T兲 ceases to be a hard anisotropy axis for large electrode widths and an applied magnetic field has the same
effect on the magnetization for different orientations within
the plane, as in the case of an extended film. Naturally, different orientations of the magnetization within the plane correspond to different AMR values, since the current is applied
along the L axis. Note that for electrode widths over 3 ␮m,
the absolute value of the normalized AMR change at saturation is the same for the three orientations of the field with
respect to the electrode axes 共⌬L = ⌬ P = ⌬T = 0.5兲. This indicates that the magnetization lies in the plane of the electrode
without a preferential orientation.
The results indicate that the magnetization of the electrodes gradually depart from the film plane for widths below
3 ␮m, reaching a maximum angle of 58° for the lowest
electrode width studied here 共w = 100 nm兲. Note that an outof-the-plane equilibrium configuration of the magnetization
has already been observed in thin 100 nm-wide Pd0.6Ni0.4 at
low temperature.3 For large electrode widths, the situation
becomes equivalent to the one found by FMR measurements
on extended thin films, indicating that the lateral constriction
of the electrodes forces the magnetization to lie out of the
plane, allowing a geometrical control of the magnetization
direction of PdNi ferromagnetic electrodes. We deduce that
the constrained lateral dimension of the electrode modifies
the demagnetizing fields of the device allowing the uniaxial
anisotropy of the PdNi film to overcome the magnetostatic
energy, pulling the magnetization off plane. Note that the
small width of the electrodes generates another nonzero component of the demagnetizing vector, Nx ⬎ 0. Since, as dis-
*[email protected]
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The possibility to control the orientation of the magnetization in ferromagnetic electrodes is of crucial importance
for producing efficient spin-transfer devices. Our results
show that in PdNi alloy ferromagnetic thin films this can be
achieved by tuning the geometry of the electrode. Specifically, the magnetization of Pd0.4Ni0.6 electrodes can be engineered to transit from in-plane to out-of-the-plane 共up to 58°兲
by varying the electrode width from 3 ␮m down to 100 nm,
respectively. The demonstrated tunability of this material
could be used to fabricate planar devices in which different
electrodes show different magnetization directions, allowing
to probe the physics of spin transfer seen in all-metallic spin
valves now in carbon-based devices, which could eventually
lead to novel applications in emerging nanotechnologies.
We want to acknowledge fruitful discussions with JeanMarc L. Beaujour and Werner Keune. J.C.G-P. acknowledges
support from UCF Undergraduate Research Initiative program. J.C.G-P., J.J.H., and E.d.B acknowledge support from
the U.S. National Science Foundation 共Grants No.
DMR0706183 and DMR0747587兲.
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The average effective value of the g-factor is 2.3 for the thickness range studied. This value is larger than the Landé g-factor
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